Roller stress slice method calculation method based on conjugate gradient

Abstract

This invention discloses a roller stress slice calculation method based on conjugate gradients. It collects the geometric, material, and load parameters of the rollers and raceways; discretizes the roller generatrix using geometric series non-equidistant slices, and refines the edge region to improve the accuracy of stress concentration calculation; solves the compliance factor between slices using Gauss-Legendé numerical integration; constructs a contact objective function based on the minimum complementary energy principle; iteratively solves the contact stress using the Fletcher-Reeves conjugate gradient method; and achieves nonlinear contact stability by correcting the contact gap, scaling the load proportionally, and updating the contact half-width with low relaxation. The axial stress distribution is output after the pressure and load errors satisfy the criteria. This method has low computational complexity and small memory footprint, and is adaptable to cylindrical / tapered rollers, generatrix modification, and roller off-center loading conditions, balancing computational efficiency and solution accuracy. It provides an efficient numerical means for bearing roller strength verification and profile optimization.

Description

Technical Field

[0001] This invention belongs to the field of numerical calculation technology of bearing roller contact mechanics, specifically involving a roller stress slice calculation method based on an improved conjugate gradient, which is particularly suitable for calculating the contact stress distribution of various bearing rollers such as cylindrical rollers and tapered rollers. Background Technology

[0002] The slice method is a classic engineering method for calculating the contact stress and load distribution of roller bearings. Its core principle is to discretize the roller along its axial generatrix into multiple micro-segments (slices), treating each slice as an independent short cylindrical roller. Local contact deformation and stress are calculated using Hertz contact theory, and then the stress distribution of the entire roller is iteratively solved by combining deformation compatibility and force balance conditions. According to relevant knowledge of elasticity mechanics and the Boussinesq solution, the mutual influence between the individual short cylinders cannot be ignored. As indicated in Luo Jiwei's related literature "Analysis, Calculation and Application of Rolling Bearings," currently, the iterative solution of the slice method considering mutual influence mainly employs three methods: fixed relaxation iteration, Newton-Raphson iteration, or force balance correction iteration. Among these methods, fixed relaxation iteration is robust and simple to implement, but its convergence speed is slow, especially when the number of slices is large, the number of iteration steps increases significantly, and the computational efficiency is low. Newton-Raphson iteration has fast convergence speed and high accuracy, but it requires the construction and solution of the Jacobian matrix, resulting in high code complexity. In strongly nonlinear scenarios, a damping factor needs to be introduced to avoid divergence, which places high demands on parameter settings. Force balance correction iteration is simple and fast, but it is only suitable for straight rollers without deformation or bending, and its robustness is poor, making it unsuitable for complex working conditions such as roller deformation and off-center loading commonly encountered in engineering. The conjugate gradient method (CG) is an efficient algorithm for solving symmetric positive definite linear equations, with the advantages of low computational complexity and small memory footprint. However, it is only applicable to linear equations, while the core of the slice method is a nonlinear contact problem. Directly applying the conjugate gradient method will lead to large linearization errors, slow convergence, and even divergence. When the roller has deformation, edge contact, or other conditions that increase the condition number of the stiffness matrix, the convergence efficiency drops significantly, failing to meet the requirements of high-precision and fast calculation in engineering. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a roller stress slice calculation method based on conjugate gradient. The method is simple and efficient, and can quickly and accurately solve the contact stress distribution of the roller along the axial direction, achieving efficient calculation of roller stress distribution and demonstrating good performance.

[0004] To achieve the above objectives, the present invention provides a roller stress slice calculation method based on conjugate gradient, comprising the following steps: S1, obtaining the geometric parameters, material parameters, and external load parameters of the roller and raceway, wherein the geometric parameters include roller length, roller diameter, roller generatrix modification function, raceway curvature radius, and contact angle; the material parameters include elastic modulus and Poisson's ratio; and the external load parameters include the total normal load of the roller. S2, the roller is uniformly discretized into n slices along the axial generatrix using the slicing method; S3, calculate the compliance influence factor between each slice based on the contact half-width; S4, calculate the surface deformation by convolution summation based on stress distribution and compliance coefficient; S5, calculate the conjugate gradient direction and step size based on the deformation, shaping amount, and initial gap; S6. After correcting the stress distribution using the conjugate gradient method, scale down the stress distribution proportionally according to the ratio of the sum of the slice loads to the applied load. Determine whether the stress distribution before and after scaling down meets the convergence condition. If the convergence criterion is met, output the roller stress distribution result. If not, use low relaxation to correct the contact half-width, return to step S3, update the influence coefficient, and repeat steps S3 to S6 until the convergence criterion is met.

[0005] As a further feature of the present invention, step S2 employs unequal-distance slicing, specifically including the following steps: S21, select the slice scaling factor r and the total number of slices n+1, where n+1 is a power of 2; S22, based on the effective roller length Lwe, scaling factor r, and total number of slices n+1, calculates the half-width of the closest slice in the roller core using a geometric series summation formula. S23, using the geometric series formula, calculate the half-width hj of a one-sided (0~(n+1) / 2-1) unequally spaced slice. S24, symmetrically obtained slice width on the other side .

[0006] As a further provision of the present invention, in step S3, the Gauss-Legendal integral formula is used to calculate the compliance influence factor, specifically including: S31, Establish the integral expression for the compliance coefficient of the slice model: ; S32, by substitution, the integration interval is transformed to [-1, 1]; the Gauss-Legend quadrature formula and quadrature coefficients are as follows: Legendre polynomial in the formula It is about the weight function on the interval [-1, 1] Orthogonal polynomials; For the integral over the general interval [a, b] By substitution of variables: Transform into an integral over the interval [-1, 1]: ; S33, select the Gauss-Legend quadrature formula with 4 nodes or 8 nodes, combine the corresponding node xi and quadrature coefficient Ai, numerically solve the integral term, and obtain the compliance influence factor between each slice; use the symmetry of the integral interval to simplify the calculation. Depending on the node division, for The integrals can be briefly described as follows: For interval In the case of dividing into 8 nodes: make : Record If we take n=7, then: Since the stress circumferential direction of any slice follows the Hertz distribution and the contact half-width is symmetrical, it can be known that The integral interval (-aj, aj) is symmetric about the origin, and can be simplified to: For interval In the case of partitioning into 4 nodes: make Depend on The symmetry of the integration interval gives: Record If we take n=3, then: .

[0007] As a further provision of the present invention, in steps S5 to S6, the iterative process of the improved conjugate gradient method includes: S51, the contact problem yields the following objective function using the variational principle. S52, Assign initial values: Given an initial pressure vector The iteration accuracy and initial pressure are chosen based on the Hertzian line contact theory solution, due to the equivalent contact radius along the generatrix of the tapered roller. The difference leads to the conclusion that: In the formula For the equivalent elasticity model, Number of slices — represents the slice width. The equivalent contact radius of the slice center In the formula For the large end radius, For the small end radius, ; S53, Calculate the deformation vector V: S54, determine the conjugate gradient direction at step k. In the formula: For the objective function About stress The partial derivative, i.e., the contact gap. , For the first Step iteration, For coefficients; Calculate the contact area Average contact gap within For contact gap Make corrections to satisfy the constraints. hour, : The coefficients are then obtained using the Fletcher-Reeves method. : S55, determine the first Step along the conjugate gradient direction Correction pressure step size : intermediate variables for: In the formula: Contact area The mean within; S56, Correcting Pressure : In the formula: The elements of the pressure vector obtained from the previous convergence. S57, Calculate the pressure iteration error and load balance error: In the formula The contact half-width obtained from the previous convergence; if or If the iteration continues, the iteration will continue; otherwise, the iteration will stop.

[0008] As a further feature of the present invention, in step S6, the contact half-width is corrected. And correct the stress again. With this setup, the traditional Gaussian elimination method has a time complexity of O(n³), and the computational cost increases dramatically with the number of slices, making it difficult to meet the fast computational requirements of large rollers and multi-slice scenarios. This invention employs the conjugate gradient method, reducing the time complexity to O(kn²), where the number of iterations k is much smaller than the number of slices n, and the acceleration effect is more significant as the matrix size increases. Combined with the Gauss-Legend high-precision numerical integration for rapid solution of the compliance influence factor, it further reduces the iterative computational overhead, resulting in a significant improvement in overall computational efficiency compared to traditional methods, and enabling efficient processing of large-scale discrete models. Existing equidistant slicing methods require densifying the entire domain slices to ensure the accuracy of edge stress calculation, leading to a surge in computational cost; sparse slicing makes it difficult to accurately capture the edge stress concentration phenomenon at both ends of the roller. This invention uses unequal-distance slicing, densifying the roller edge region and sparse core region through a geometric sequence, reducing the total number of slices while accurately characterizing the edge stress gradient changes, effectively improving the computational accuracy of edge stress concentration regions, and ensuring the accuracy of the overall stress distribution. Traditional fixed relaxation iteration methods suffer from slow convergence speed and numerous iteration steps; Newton-Raphson iteration exhibits poor robustness and is prone to divergence under strongly nonlinear conditions; force balance correction iteration has a narrow applicability and cannot adapt to complex scenarios such as roller profile modification and off-center loading. This invention makes targeted improvements to the conjugate gradient method, effectively adapting to the nonlinear contact characteristics of the slicing method through strategies such as contact gap correction, proportional load scaling, and low-relaxation contact half-width update. It exhibits strong convergence stability, is less prone to divergence, and can stably solve stress distributions under complex conditions such as roller generatrix modification, edge contact, and off-center roller loading, thus broadening its engineering applicability. Traditional iterative algorithms require constructing and storing large Jacobian matrices or complete coefficient matrices, resulting in high memory consumption. This invention employs the conjugate gradient method for iterative solution, eliminating the need to store complete high-order matrices; only vector data needs to be updated during iteration, significantly reducing memory usage and computational requirements. This method is applicable not only to contact stress calculations in cylindrical roller bearings but also to various other bearing rollers, such as tapered roller bearings. It effectively handles common roller profile modification conditions such as logarithmic profiles and single circular arc profiles, providing fast and high-precision numerical calculation support for the structural design, strength verification, and performance optimization of bearing rollers, thus possessing significant engineering application value. The invention also reduces hardware requirements, facilitating efficient computation on ordinary computers. Attached Figure Description

[0009] Figure 1 This is a simplified diagram of the line contact of a tapered roller bearing according to an embodiment of the present invention; Figure 2 This is a diagram of the slicing model according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the roller and raceway states according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the roller tilt and inner raceway state according to an embodiment of the present invention; Figure 5This is a schematic diagram of coordinate transformation under the roller tilting condition according to an embodiment of the present invention. Detailed Implementation

[0010] This invention provides an embodiment of a roller stress slice method based on conjugate gradient. The contact model between the roller and the raceway can be viewed as a series of rectangular blocks in contact with an elastic semi-infinite body, with the load concentrated at the center of a single rectangular block. Cylindrical rollers can be considered a special case of tapered rollers. The improved algorithm will now be explained using tapered rollers as an example.

[0011] Dry contact assumption: There is no friction between the rectangular block and the elastic semi-infinite body; the contact interface is not subjected to tensile stress.

[0012] The fundamental equation assuming point contact is: In the formula For the equivalent elastic modulus, For contact stress, Initial gap Without making any assumptions about the initial clearance z(x,y) and contact stress p(x,y) between the contact surfaces, the equations are universally applicable to elastic contact problems in non-close contact states, and naturally include the contact problem between the rollers and raceways of tapered roller bearings. In general, the above basic equations are difficult to solve theoretically and are usually solved numerically. However, the coefficient matrix in the contact problem is a well-defined symmetric positive definite matrix, so the conjugate gradient method can be used to solve it.

[0013] The slice model is a one-dimensional treatment of finite-length contact problems and is well-suited for contact problems with narrow contact regions.

[0014] 1.1 Basic Equations Based on the understanding of line contact problems, the line contact problem of tapered roller bearings can be further simplified, such as... Figure 1 As shown, the possible contact area is divided into n+1 strip elements along the generatrix direction of the roller (positive x-direction points to the small end of the roller, negative x-direction points to the large end of the roller). Within element j, it is assumed that the contact stress is uniformly distributed along the generatrix direction and distributed according to Hertz along the circumferential direction (y-direction). Then, the roller line contact form can be derived from the basic equations of point contact as follows: In the formula The maximum contact stress is at the center of the element. Given a unit Hertz contact half-width, we have: The compliance coefficient is defined as follows: Will right Points, get Calculate the compliance coefficient Numerical integration is required; see section 2.2.4 for details. The basic equations of the aforementioned slice model mainly consist of two parts: stress balance equations and deformation compatibility equations. However, the deformation compatibility equations are only satisfied within the actual contact area, while the solution domain of the selected slice model is larger than the actual contact area. Therefore, if a set of deformation compatibility equations is listed, slice elements in a non-contact state must be removed from the equation set during the iteration process before iteration can be performed to ensure that all elements in the equation set satisfy the deformation compatibility equations.

[0015] In other words, the contact gap is zero during contact deformation, but not zero when there is no contact. Therefore, the contact gap is introduced into the deformation compatibility equation. A new equation is constructed that satisfies both contact and non-contact elements, thus avoiding the tedious process of element removal. The new equation containing the contact gap and the corresponding constraints are as follows: Comparing the contact gap equation and the deformation compatibility equation, it is easy to see that the contact gap equation is an extension of the deformation compatibility equation, while the deformation compatibility equation is the contact deformation equation. A special case when zero is taken. Therefore, the deformation compatibility equations for the contact problem are rewritten, and the contact clearance and contact stress between the roller and the raceway surface satisfy the following equations and constraints: In the formula For the gap between contact surfaces This represents the approach distance of a rigid body (elastic approximation). For the geometry of the contact body (roller and raceway profile design / roller tilt angle) Surface elastic deformation matrix elements In programming languages, the first element of a matrix or vector is either (0, 0) or (0). To maintain consistency with the calculation program and facilitate code mapping, rows and columns in a matrix start from 0, i.e.: , is an n+1 vector.

[0016] Based on the constraints and the contact surface clearance equation, the above problem can be considered a linear complementary problem (LCP), which can be expressed in matrix form: In the formula constant vector The above matrix expression represents the displacement field function for the contact problem. According to the principle of minimum complementary energy: within an elastic body satisfying the equilibrium differential equations, among all allowable stress states satisfying the stress boundary conditions on the stress boundary, the true stress state (the stress satisfying the deformation compatibility condition) must have its total complementary energy functional minimized. The total complementary energy functional of the slice model, i.e., the objective function, is constructed using the variational principle as follows: Therefore, the linear complementarity problem is equivalent to finding the minimum value of the objective function under constraints. In the solution of the tapered roller, the equivalent contact radius of the contact element in the direction of the roller generatrix varies due to the influence of the roller taper. Therefore, the coefficient matrix K of the slice model is an asymmetric positive definite matrix.

[0017] The conjugate gradient method is used to numerically solve the objective function (a quadratic function). This is achieved by resolving the solution function during each iteration. Elements less than 0 are truncated. exist When the value is greater than 0, the mean is subtracted to approximate 0; when the value is less than 0, no negative value is taken, thus satisfying the constraint conditions.

[0018] 1.2 Slice Division For small rollers, increasing the number of slices can ensure accurate results. However, if the rollers are large, the required number of slices will limit computational efficiency. Relevant literature indicates that the elastic approximation of the roller and the stress distribution at its core are not sensitive to the number of slices. However, when edge stress concentration occurs, the thickness of the slices has a significant impact on the edge stress, requiring more slices to ensure accurate results.

[0019] Equal-interval partitioning of the slice model is the simplest partitioning method, but it has poor computational efficiency for edge stress problems; for example Figure 2 As shown, the unequal-spacing slicing model can refine the edge mesh of the roller, which not only ensures the accuracy of the results but also reduces the number of slices and improves the computational efficiency.

[0020] With n+1 slices, the half-width of a grid with equal dimensions can be simply represented as: Based on different encryption methods, they are divided into two categories: arithmetic sequence encryption and geometric sequence encryption. To better control the width of the roller slices, a geometric sequence encryption method is proposed, as follows: (1) Select the slice scaling factor r and the number of slices n+1 according to the requirements, and the number of slices n+1 is a power of 2; (2) Given the effective length L of the roller we The scaling factor r and the number of slices n+1 can be used to calculate the half-width of the densest slice located at the center of the model using the formula for summation of a geometric series. (3) Calculate the half-width hj of a one-sided (0~(n+1) / 2-1) unequally spaced slice using the geometric series formula; (4) Obtain the width of the slice on the other side symmetrically. 1.3 Gauss-Legend Integral for Finding the Coefficient Matrix The formula for the compliance coefficient of the slice model is: The formula contains integral terms, making analytical solutions for calculating its influence coefficients difficult. Numerical integration methods can be used. This paper employs the Gauss-Legendal integral to solve for the influence coefficients.

[0021] The Gauss-Legend quadrature formula and quadrature coefficients are as follows: Legendre polynomial in the formula It is about the weight function on the interval [-1, 1] Orthogonal polynomials.

[0022] For the integral over the general interval [a, b] By substitution of variables: Transform into an integral over the interval [-1, 1]: The Gauss-Legend quadrature formula can then be used to calculate the quadrature. The nodes xi and quadrature coefficients Ai are shown in the table.

[0023] Depending on the node division, for The integrals can be briefly described as follows: (1) For intervals Divide into 8 nodes: make : Record If we take n=7, then: Since the stress circumferential direction of any slice follows the Hertz distribution and the contact half-width is symmetrical, it can be known that The integral interval (-aj, aj) is symmetric about the origin, and can be simplified to: (2) For intervals Divide into 4 nodes: make Depend on The symmetry of the integration interval gives: Record If we take n=3, then: 1.4 Roller profile and simplified tilt angle Define the inner raceway geometry vector as follows: The geometric vector of the roller is Contact geometric vectors : When the rollers and raceways tilt, such as Figure 3 For example, calculate the contact geometry matrix. .

[0024] When the large end of the roller tilts towards the inner ring, it can be considered that the geometric shape vector of the roller is: The inner raceway geometry vector changes due to the tilt angle. The rotation remains unchanged, and the roller rotates about the midpoint of the contact generatrix, rather than the geometric center of the roller.

[0025] The slice model uses a simplified tilt angle to correct for the drop in profile. For example... Figure 4 and Figure 5 As shown, without considering the slice model The changes after the axis (along the generatrix) tilts are considered only. The change in drop along the axial direction is used to calculate the geometric vector of the tilted roller: Let the slice coordinates located on the contact generatrix in the slice model be... , Indicates the position of the slice center in the direction of the contact generatrix; The corresponding normal drop in the profile is Without considering tilt, we have: . If the origin of the spatial coordinate system is located at the center of the contact generatrix, then in In the plane, the coordinates of the tilted slice ,have: In the formula: The angle of inclination. Effective length of the roller Roller profile normal drop It is mainly determined by the following formula: Logarithmic curve: In the formula Design load for the normal direction of the roller raceway.

[0026] Single circular arc line: In the formula This refers to the radius parameter for the unit arc modification.

[0027] 1.5 Conjugate Gradient Method The contact problem yields the following objective function based on the variational principle. The conjugate gradient method is then used to find the minimum value of the objective function under constraints.

[0028] Aside from the difference in solving the deformation matrix during iteration, the iterative process of the conjugate gradient method for the slice model is basically the same as that for the mesh model. The specific process is as follows: (1) Assigning initial values: Given an initial pressure vector Iteration accuracy. The initial pressure is chosen from the Hertzian line contact theory solution, due to the equivalent contact radius in the generatrix direction of the tapered roller. They are different, therefore: In the formula For the equivalent elasticity model, Number of slices The slice width, The equivalent contact radius of the slice center In the formula For the large end radius, For the small end radius, .

[0029] (2) Calculate the deformation vector V: (3) Determine the conjugate gradient direction at step k. In the formula: For the objective function About stress The partial derivative, i.e., the contact gap. , For the first Step iteration, coefficient Calculate the contact area Average contact gap within For contact gap Make corrections to satisfy the constraints. hour, : Then the coefficient For (Fletcher-Reeves method): (4) Determine the first Step along the conjugate gradient direction Correction pressure step size : intermediate variables for: In the formula: Contact area The mean within.

[0030] (5) Correction pressure : In the formula: The elements of the pressure vector obtained from the previous convergence. (6) Calculate the pressure iteration error and load balance error: In the formula This is the contact half-width obtained from the previous convergence.

[0031] if or If the iteration continues, the iteration will continue; otherwise, the iteration will stop.

[0032] (7) Correcting the contact half-width And correct the stress again. The above examples are merely one preferred embodiment of the present invention. Ordinary variations and substitutions made by those skilled in the art within the scope of the technical solution of the present invention are all included within the protection scope of the present invention.

Claims

1. A method for calculating roller stress slices based on conjugate gradients, characterized in that: The process includes the following steps: S1, obtaining the geometric parameters, material parameters, and external load parameters of the roller and raceway. The geometric parameters include roller length, roller diameter, roller generatrix modification function, raceway curvature radius, and contact angle. The material parameters include elastic modulus and Poisson's ratio. The external load parameters include the total normal load on the roller. S2, the roller is uniformly discretized into n slices along the axial generatrix using the slicing method; S3, calculate the compliance influence factor between each slice based on the contact half-width; S4, calculate the surface deformation by convolution summation based on stress distribution and compliance coefficient; S5, calculate the conjugate gradient direction and step size based on the deformation, shaping amount, and initial gap; S6. After correcting the stress distribution using the conjugate gradient method, scale down the stress distribution proportionally according to the ratio of the sum of the slice loads to the applied load. Determine whether the stress distribution before and after scaling down meets the convergence condition. If the convergence criterion is met, output the roller stress distribution result. If not, use low relaxation to correct the contact half-width, return to step S3, update the influence coefficient, and repeat steps S3 to S6 until the convergence criterion is met.

2. The roller stress slice calculation method based on conjugate gradient according to claim 1, characterized in that: In step S2, unequal-distance slices are used for partitioning, specifically including the following steps: S21, select the slice scaling factor r and the total number of slices n+1, where n+1 is a power of 2; S22, based on the effective roller length Lwe, scaling factor r, and total number of slices n+1, calculates the half-width of the closest slice in the roller core using a geometric series summation formula. S23, using the geometric series formula, calculate the half-width hj of a one-sided (0~(n+1) / 2-1) unequally spaced slice. S24, symmetrically obtained slice width on the other side 。 3. The roller stress slice calculation method based on conjugate gradient according to claim 1, characterized in that: In step S3, the Gauss-Legend de Gauss integral formula is used to calculate the compliance influence factor, specifically including: S31, Establish the integral expression for the compliance coefficient of the slice model: ； S32, by substitution, the integration interval is transformed to [-1, 1]; the Gauss-Legend quadrature formula and quadrature coefficients are as follows: Legendre polynomial in the formula It is about the weight function on the interval [-1, 1] Orthogonal polynomials; For the integral over the general interval [a, b] By substitution of variables: Transform into an integral over the interval [-1, 1]: ； S33, select the Gauss-Legend quadrature formula with 4 nodes or 8 nodes, combine the corresponding node xi and quadrature coefficient Ai, numerically solve the integral term, and obtain the compliance influence factor between each slice; use the symmetry of the integral interval to simplify the calculation. Depending on the node division, for The integrals can be briefly described as follows: For interval In the case of dividing into 8 nodes: make : Record If we take n=7, then: Since the stress circumferential direction of any slice follows the Hertz distribution and the contact half-width is symmetrical, it can be known that The integral interval (-aj, aj) is symmetric about the origin, and can be simplified to: For interval In the case of partitioning into 4 nodes: make Depend on The symmetry of the integration interval gives: Record If we take n=3, then: 。 4. The roller stress slice calculation method based on conjugate gradient according to claim 1, characterized in that: In steps S5-S6, the iterative process of the improved conjugate gradient method includes: S51, the contact problem yields the following objective function using the variational principle. S52, Assign initial values: Given an initial pressure vector The iteration accuracy and initial pressure are chosen based on the Hertzian line contact theory solution, due to the equivalent contact radius along the generatrix of the tapered roller. The difference leads to the conclusion that: In the formula For the equivalent elasticity model, Number of slices — represents the slice width. The equivalent contact radius of the slice center In the formula For the large end radius, For the small end radius, ; S53, Calculate the deformation vector V: S54, determine the conjugate gradient direction at step k. In the formula: For the objective function About stress The partial derivative, i.e., the contact gap. , For the first Step iteration, For coefficients; Calculate the contact area Average contact gap within For contact gap Make corrections to satisfy the constraints. hour, : The coefficients are then obtained using the Fletcher-Reeves method. : S55, determine the first Step along the conjugate gradient direction Correction pressure step size : intermediate variables for: In the formula: Contact area The mean within; S56, Correcting Pressure : In the formula: The elements of the pressure vector obtained from the previous convergence. S57, Calculate the pressure iteration error and load balance error: In the formula The contact half-width obtained from the previous convergence; if or If the iteration continues, the iteration will continue; otherwise, the iteration will stop.

5. The roller stress slice calculation method based on conjugate gradient according to claim 4, characterized in that: In step S6, the contact half-width is corrected. And correct the stress again. 。

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